In a tin can, the ratio of the number of black marbles to the number of pink marbles was 1 : 4. Each time, 3 black and 6 pink marbles were taken out of the tin can. A while later, only 42 pink marbles were left in the tin can. What was the total number of marbles in the tin can at first?
|
Black marbles |
Pink marbles |
Before |
1x3 = 3 u |
4x3 = 12 u |
Change |
- 3 u |
- 6 u |
After |
0 |
42 |
Since there is no black marbles left, this means that the number of black marbles at first is the same as the number of black marbles taken out.
Make the number of black marbles at first and taken out the same. LCM of 1 and 3 is 3.
Number of pink marbles in the end
= 12 u - 6 u
= 6 u
6 u = 42
1 u = 42 ÷ 6 = 7
Total number of marbles in the tin can at first
= 3 u + 12 u
= 15 u
= 15 x 7
= 105
Answer: 105